A radioactive isotope of the element osmium Os-182 has a half-life of 21. 5 hours. This means that if there are 100 grams of Os-182 in a sample, after 21. 5 hours,


there will only be 50 grams of that isotope remaining.


a. Write an exponential decay function to model the amount of Os-182 in a sample over time. Use Ag for the initial amount and A for the amount after time t in hours.


(Type an exact answer. Use integers or decimals for any numbers in the equation. )

The expression for g in terms of other variables is g = Fd^2/m1m2

Given the expression below as shown

F=gm1*m2/d2

We are to make g the subject of the formula

F=gm1*m2/d2

Cross multiply

Fd2 = gm1m2

Divide both sides by m1m2

Fd^2/m1m2 = g

g = Fd^2/m1m2

Hence the expression for g in terms of other variables is g = Fd^2/m1m2

Learn more on subject of formula here: https://brainly.com/question/657646

#SPJ1

Answer:

x = 5, 1

Step-by-step explanation:

To solve for x, you must factor the equation. The factored equation will be: (x - 1) (x - 5) = 0. After factoring, isolate the two factored equations: (x - 1) = 0 and (x - 5) = 0. Then solve for x for both the equations which should get you to x = 5, 1.

The area bounded by the curve, x-axis and y-axis of the function y = √(x + 3) is 2√3

The curve is given as:

y = √(x + 3)

The area bounded by the curve, x-axis and y-axis is when x = 0 and y = 0

When y = 0, we have:

0 = √(x + 3)

This gives

x = -3

So, we set up the following integral

A = ∫ f(x) d(x) (Interval a to b)

This gives

A = ∫ √(x + 3) d(x) (Interval -3 to 0)

When the above is integrated, we have:

A = 1/3 * [2(x + 3)^(3/2)] (Interval -3 to 0)

Expand

A = 1/3 * [2(0 + 3)^3/2 - 2(-3 + 3)^3/2]

This gives

A = 1/3 * 2(3)^3/2

Apply the law of indices

A = 2(3)^1/2

Rewrite as:

A = 2√3 or 3.46

Hence, the area bounded by the curve, x-axis and y-axis of the function y = √(x + 3) is 2√3

Read more about areas at:

brainly.com/question/14115342

#SPJ1

Question:

A sample of cans of peaches was taken from a warehouse, and the content of each can mearsed for weight. the sample means was 486g with stand deviation 6g. state the weight percentage of cans with weight:

Draw normal curve to help - split into 8 section ( i can't draw it here)

a) 34.13% of cans will be between 480g and 486g.

b) 13.59 + 2.15 + 0.13= 15.87% of cans greater than 492g.

Look at the Stand Dev Graph where the give you the number

Step-by-step explanation:

Let me give you a different question and i will answer it, which you help you answer your question.

Answer: 3x - 6 (in^2)

Step-by-step explanation:

base * height / 2

=

3 ( 2x - 4) / 2 (in^2)

= 3x - 6 (in^2)

Answer: 3x-6 in^2

Step-by-step explanation:

There is no way to figure out what x is without additional information, so you have to leave the answer in this form

The linear and exponential equation that matches f(2) = 12 and f(4) = 48 are y = 18x - 24 and f(x) = 3(2)ˣ respectively

An equation is an expression that shows the relationship between two or more variables and numbers.

For the exponential function, when f(2) = 12:

12 = ab²       (1)

Also, at f(4) = 48:

48 = ab⁴   (2)

Hence:

a = 3, b = 2

f(x) = 3(2)ˣ

For the linear function using the points (2, 12) and (4, 48):

y - 12 = [(48 - 12) / (4 - 2)](x - 2)

y = 18x - 24

The linear and exponential equation that matches f(2) = 12 and f(4) = 48 are y = 18x - 24 and f(x) = 3(2)ˣ respectively

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The probability of choosing cards either Q or R when a card is drawn from a deck of 8 cards is 0.25.

Given that a card is randomly chosen from 8 cards shown in figure.

We have to calculate the probability of choosing either Q or R when a card is drawn from those 8 cards.

Probability means calculating the likeliness of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative.

Number of cards=8

Number of repeated cards=0

Number of cards showing Q and R =1 each.

Probability of getting Q or R is P(X=Q)+P(X=R)

= 1/8+1/8

=2/8

=1/4

=0.25

Hence the probability of getting either P or Q when a card is drawn from 8 cards is 0.25.

Learn more about probability at https://brainly.com/question/24756209

#SPJ1

Answer: 7:4

Step-by-step explanation:

40 boys and girls 3:2 = 24 boys + 16 girls

4 boys are added  28 boys + 16 girls /4  = 7:4

Answer:

7:11

Step-by-step explanation:

We know the total number of students and the ratio of boys to girls.  The total for the ratio of boys and girls would be 5 (3+2).  Now we can set up proportions knowing these numbers.

b = 3

g =2

t =5

Let's find out how many actual boys there are by setting up a proportion

3/5 = b/40  

I will look at the denominators to find x.  5 times what gives me 40? (8).  So, I will multiple the top number (numerators).  Since I need to multiple the bottom number by 8 to get the number 40, I will now multiple the top number by 8 and get 24.

Now, I know how many actual boys and girls were in the original class.  There were 24 boys, 16 girls (40 - 24) and 40 total students.  

Now I will take this new information and apply it to the new situation.  Now I have 28 boys (24 + 4) and a new total 44.

The ratio of boys to girls would not be 28: 16 or 7:4

Blank 1: Substitution property of equality

Blank 2: 50

Blank 3: Subtraction property of equality

The blank spaces in the task content can be filled with; Substitution property, 90° and subtraction property.

Since it follows from the vertical angles theorem that angle 1 = angle 4 as they are congruent.

Additionally, angles 1 and 2 are said to be complementary and hence, the sum of their measures is equal to 90°.

Finally, by virtue of the subtraction property of equality, the measure of angle 2 is; 90° - 40° = 50°.

Read more on complementary angles;

https://brainly.com/question/16281260

#SPJ1

Answer:

138

Step-by-step explanation:

There is 60 seconds in a minute, so if the heart beats 23 times in 10 seconds, it is 138 bpm.

23 * 6 = 138

Answer:

|-1| + |3|

Step-by-step explanation:

We can use absolute values to find the distance between positive and negative numbers on a number line.

|-1| + |3| =

Keep in mind that

- the absolute value of a positive number is positive and

- the absolute value of a negative number is positive

1 + 3 =

4 units

The resulting equation written in standard form is 16x² - 22x + 6 = 0.

Quadratic Equation in Standard Form: ax² + bx + c = 0

a, b and c are known values. a can't be 0.

"x" is the variable or unknown (we don't know it yet).

The "solutions" to the Quadratic Equation are where it is equal to zero.

They are also called "roots", or sometimes "zeros"

We can Factor the Quadratic (find what to multiply to make the Quadratic Equation)

Calculation for the given equation-

Now, y=-16x²+24x+6

Substitute, y = 12+2x in y = -16x²+24x+6.

=> 12+2x = -16x²+24x+6

=> 16x²-24x-6+12+2x = 0

=> 16x²-22x+6 = 0

Therefore, the quadratic equation given in the standard form is 16x²-22x+6 = 0.

To know more about the quadratic equation, here

https://brainly.com/question/1214333

#SPJ4

The complete question is-

The two equations are given below;

Y = 12 + 2x   linear equation

Y = -16x² + 24x + 6  quadratic equation

If you substitute 12 + 2x for y in the second equation how is the resulting equation written in standard form?

Using the Fundamental Counting Theorem, there are 15 ways to travel from Andy's house to Willie's house.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For this problem, the parameters are:

[tex]n_1 = 3, n_2 = 5[/tex].

Hence the number of ways is:

N = 3 x 5 = 15.

More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866

#SPJ1

The number of weeks it will take for the budget money to run out is; 2 weeks.

The number of weeks it would take for the budget money to decrease till it runs out as required in the task can be interpreted as the x-value which corresponds to a Y-value of zero.

Hence, by setting y=0; we have;

-2x -0 = -4

-2x = -4

Divide both sides of the equation by; -2.

x = 2

Read more on x-intercept of a linear equation;

https://brainly.com/question/4074386

#SPJ1

1.(a) The number of marigolds used in a day is 42.

 (b) The total number of flowers used by using suitable property of whole numbers is 98.

 (c) She earned Rs. 3570

2.(a) The value of [tex]819 + 364 + 181 + 436[/tex] is 1800.

 (b) The value of [tex]20 \times 348 \times 50[/tex] is 348000.

3. The value of [tex]492 \times 13 + 492 \times 37[/tex] is 24600.

4.(a) Name the property 86 + 65 = 65 + 86 is commutative property.

 (b) The multiplicative identity of whole numbers is 1.

5. The next two numbers in the pattern 1,1,2, 3,5,8 are 13 and 21.

1. (a) The number of marigolds used in a day is 42.

Rani made 7 bouquets on each day by arranging 8 roses and 6 marigolds in each bouquet. So number of marigolds used in a day is 7×6 = 42.

  (b) The total number of flowers used by using suitable property of whole numbers is 98 flowers used by using distributive property.

What is distributive property of whole numbers?

The distributive property of multiplication states that when multiplying a number by the sum/difference of 2 numbers, the final value is equal to the sum/difference of each addend multiplied by the third number.

Distributive property = a×(b+c) = a×b+a×c

Total number of flowers = 7×(8+6) = 7×14 = 98.

(c) If she sold 42 bouquets in a whole week, find the amount she earned is  rs.3570.

Each bouquet was sold for Rs.85. Then she earned a whole week off = 42×85 = rs.3570.

2. (a)  By suitable rearrangement, the value of 819 + 364 + 181 + 436 is 1800.

Rearrangement of the given numbers = (819+181)+(364+436)

                                                               = 1000+800

                                                               = 1800    

   (b)  By suitable rearrangement, the value of 20 x 348 x 50 is 348000.

Rearrangement of the given numbers = 348×(50×20)

                                                               = 348×1000

                                                               = 348000  

3.  Using suitable property find the value of 492 x 13 + 492 x 37 is 24600 by using distributive property.

By using distributive property = 492 x 13 + 492 x 37

                                                   = 492×(13+37)

                                                  = 492×50

                                                  = 24600

4. (a) Name the property 86 + 65 = 65 + 86 is commutative property.

What is commutative property?

This law simply states that with addition and multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answer.

By using commutative property,  a+b = b+a

   86 + 65 = 65 + 86

          151 = 151                            

   (b)  The multiplicative identity of whole numbers is 1.

Multiplying a whole number by 1 equals that identical number, the whole number 1 is called the multiplicative identity.

5.  The next two numbers in the pattern 1,1,2, 3,5,8,?,? are 13 and 21.

Just add the no before the given no then you will get the pattern. example first no=1 and no before it is 0

1+0=1

1+1=2

2+1=3

3+2=5

5+3=8

8+5=13

Hence, The next two numbers for the given series are 13 and 21.

To learn more about commutative property from the given link

https://brainly.com/question/778086

#SPJ4

The margin of error of this poll is

Given that 230 people were asked if they liked dogs, and 90% said they did.

In a random sample, a margin of error is a statistical measure that takes into account the discrepancy between actual and expected results.

Sample size (N)=230

Sample proportion  [tex](\hat{p})[/tex] = 90% = 0.90  and

confidence interval = 99%

The critical value at 99% confidence interval with α=0.01 is

[tex]\begin{aligned}Z_{c}&=Z_{1-\frac{\alpha}{2}}\\ &=Z_{1-\frac{0.01}{2}}\\ &=Z_{0.995}\\ &=2.576\end[/tex]

This value is taken from the Standard normal distribution table.

Now, we will calculate the margin of error (E) by using the formula

[tex]E=Z_{c}\sqrt{\frac{\hat{p}(1-\hat{p})}{N}}[/tex]

Substituting the values in the formula, we get

[tex]\begin{aligned}E &=2.576\times \sqrt{\frac{0.90(1-0.90)}{230}}\\ &=2.576\times \sqrt{\frac{0.09}{230}}\\ &=2.576\times\sqrt{0.00039}\\ &=2.576\times 0.0197\\ &=0.0507\end[/tex]

Hence, the margin of error when 230 people were asked if they liked dogs, and 90% said they did is 0.0507.

Learn more about margin of error from here brainly.com/question/25779324

#SPJ4

Part A - Tara cuts [tex]12[/tex] pieces of [tex]2/5[/tex] from [tex]4\frac{4}{5}[/tex] feet of rope.

Part B - The quotient means the amount of foot pieces so it is [tex]12[/tex] foot pieces.

How can we find the foot pieces of [tex]2/5[/tex] from [tex]4\frac{4}{5}[/tex]  rope. ?

from part A

we solve the fraction

[tex]4\frac{4}{5} =24/5[/tex] rope

And Tara needs to pieces of [tex]2/5[/tex] foot

So we need to divide

[tex]\frac{24/5}{2/5} \\=\frac{24}{5} *\frac{5}{2} \\=\frac{24}{2} \\=12[/tex]

For part B

When we using the information from part A we decide that the quotient means the amount of foot pieces Tara can cut from the [tex]4\frac{4}{5}[/tex] feet of rope.

Learn more about the pieces of rope is here:

https://brainly.com/question/28048536

#SPJ4

I am the number 4052. It is rather confusing and i cannot promise that it is correct. Hope it helps : )

The possible amount of time, in minutes, that it could take the worker to box 168 pairs of shoes is between 14 minutes to 21 minutes.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

A worker at a shoe factory is required to box at least 8 pairs of shoes per minute, and not more than 12 pairs of shoes per minute.

For 168 pairs of shoe:

Maximum time = 168 pair / 8 pairs per minute = 21 minutes

Minimum time = 168 pair / 12 pairs per minute = 14 minutes

The possible amount of time, in minutes, that it could take the worker to box 168 pairs of shoes is between 14 minutes to 21 minutes.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The complete equation so that the statement is true is 3x+9+4x+x= 8x + 1

The equation is given as:

3x+9+4x+x=

Represent the blank with y

So, we have:

3x + 9 + 4x + x = y

Evaluate the like terms

8x + 9 = y

For the equation to have no solution the value of y and 8x + 9 must not be equal.

Take for instance

y = 8x + 1

So, we have:

8x + 9 = 8x + 1

Subtract 8x from both sides

9 = 1

The above equation is false because 1 and 9 are not equal

Hence, the complete equation so that the statement is true is 3x+9+4x+x= 8x + 1

Read more about equations at:

https://brainly.com/question/7784687

#SPJ1

Complete question

Use the drop-down menus to complete each equation so the statement about its solution is true.

No Solutions

3x+9+4x+x=

The confidence interval formula is extremely complicated to derive, which is one of the justifications for using the bootstrap approach. this statement is true.

A resampling technology named the bootstrap can be used to sample a dataset using replacement to calculate statistics on a group. Estimating summary statistics like the mean or standard deviation may be done using it.

The benefits of bootstrapping include its simplicity in estimating standard errors and confidence intervals as well as its cost-effectiveness in avoiding the need to conduct the operation to get additional groups of sampled data.

Therefore it can be concluded that the said query statement is true.

Learn more about the bootstrap-related problems here:

https://brainly.com/question/15558134

#SPJ4

Answer:

8 minutes.

Step-by-step explanation:

We work in fractions of the wall they can paint in 1 minute, so

1/12 + 1/24 = 1/x  where x is the time it takes when working together.

Multiplying through by 24x:

2x + 1x = 24

3x = 24

x = 8 minutes.

Answer:

V=  (pi) (r squared) (h)

Step-by-step explanation:

Answer:

The unit of measuring volume of the sphere is cubic meters.

Solving the given equation, the value of v that makes the statement true is:

A. v = 8.

The equation is:

[tex]12 = 12 + \frac{v - 8}{2}[/tex]

Hence:

[tex]\frac{v - 8}{2} = 0[/tex]

Applying cross multiplication:

v - 8 = 0

v = 8.

Hence option A is correct.

More can be learned about equations at https://brainly.com/question/27882730

#SPJ1

Step-by-step explanation:

well, as you can witness both of the equations are equal to y, so you're free to reckon that they are equal as well

[tex]6x - 3 = 2x + 17 = = = > \\ 4x = 20 = = = > x = 5 \: and \: \\ y = 6(5) - 3= = = > y = 27[/tex]

Answer:

<3

Step-by-step explanation:

5, 27 is right on acellus

x=5

y=27

The  kind of statistical study the zoologist conducted was D. observational study.

An observational study  serves as a study  whereby the researcher simply observes the subjects without interfering with it.

This is different from carrying out experiment on them or just a theoretical approach.

Learn more about research on:

https://brainly.com/question/968894

#SPJ1

CHECK THE COMPLETE QUESTION BELOW:

A zoologist researched the feeding habits of lemurs. She collected data by studying the lemurs in a zoo exhibit for a one-month period and drew conclusions based on her data. What kind of statistical study did the zoologist conduct? A. survey B. theoretical study C. experiment D. observational study

Using the law of sines, it is found that 1 triangle can be formed with the given conditions.

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

Hence, for this problem, we have that the relation is:

[tex]\frac{\sin{64^\circ}}{10} = \frac{\sin{G}}{9}[/tex]

[tex]\sin{G} = 0.9\sin{64^\circ}[/tex]

[tex]\sin{G} = 0.8089[/tex]

[tex]G = \arcsin{0.8089}[/tex]

G = 54º

A triangle can have one angle of 64º and another of 54º, hence 1 triangle can be formed with the given conditions.

More can be learned about the law of sines at https://brainly.com/question/25535771

#SPJ1

Answer:

$4.86

Step-by-step explanation:

Original price: $5.40

Discount: 10%

Discount amount:

10% of $5.40 = 0.1 × $5.40 = $0.54

Discounted price:

$5.40 - $0.54 = $4.86

Answer:

$4.86

Step-by-step explanation:

There are two approaches to this problem.

1:

You can multiply the original value by 10% and subtract it from the original value. In this case, $5.40-(5.40×10%). This becomes $5.40-$0.54. This is $4.86.

2:

You can simply multiply the original value by 90%. In this case, $5.40×90%. This also becomes $4.86.

Using the unit circle, the correct answer regarding the comparison of angles w and t is given by:

a. t > w.

For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].

From this, we get that the sine is represented by the vertical axis. As we advance into the second quadrant, as the angle increases, sine decreases. Hence, since sin w > sin t, we have that t > w and option a is correct.

More can be learned about the unit circle at https://brainly.com/question/16852127

#SPJ1